March 19, 2018

x log x12345678910

Round to thousandths

log 3 + log 5 log (3*5)log 2 + log 8 log (2*8)log 9 + log 6 log (9*6)

8.4 d10

log 1=0 log ,o10=XProperties Bol

of -477 10=10a 602

Logs :399g 10=1.

845.903.1954

b-

=. 477.699=1%1*77%8⇐ log 152 I. 176

a-→ == .

9541=778--1.732

A >OB > o

←addition

log At log B = logCAB)Same base

March 19, 2018

Based on your findings on the previous pageComplete the following statement:

Now, make a conjecture.

log ( Min ) Product

Property.

Quotientlog IFu) Property

March 19, 2018

Properties of Logarithms

Product Property

Quotient Property

Power Property

Seeprevious Page

.

f

log ME x log M

These properties can be appliedto logarithms of any base

March 19, 2018

State the property or properties used to rewrite each expression

' ' o

?⇐ z

→ T.ge#=logz2

→

FFsaBtBB¥¥¥; property

'

;¥Ilogs czpyrgduotproperty

March 19, 2018

Write each logarithmic expression as a single logarithm

⇒¥÷÷÷

iasmmm÷÷÷÷÷÷÷"

3 logb

4 - 3 logy 2-

3 log ,22 - 3 log

,2

610%2 - 3 log ,2

= I

310%2 = log,

23 -- logy,

8

d

→ 3 log ,Xt

loggywrite as a" ¥::::::::④ 10%641Apply the power propertybefore applying the

Product or Quotient Properties

March 19, 2018

Expand each logarithm

(a) = log,

a' Flog,b "=3 log ,

at 410g,b

= log 27 t log zb

°=log y②- log32=2 logy - log 9I

+ \ 2 log1=2 (logy - logs)T = 2 logy -2 log 3

March 19, 2018

Loudness of Sounds

L=,'¥I - intensityof sound in

Io a lowest intensity sound for a human

[ = loudness ofsound findB )

March 19, 2018

-

=LI

,= present intensity

Iz=.5i÷:::÷:

:÷*h=m'¥Lz = reduced loudness 12=10 log II *

µ 4 - La = change in dB Io

- e ←

to log- 10 log 'I÷ → 1010g '¥ - blog

- -

loflog log !I÷)→10 (log -- lofog

HOClog # )=lO( log 2)

March 19, 2018carotene,

T O r

"

-

- .

IT log Z - I, log

3 - I log X

log Z"4 - log 344 - log x

"

-

log ,) -log x

"

= log IFE- log x

5k

log = log HE. x - 5h )T log ¢"

4 j ki ×- 5h )

March 19, 2018

a,eMEEq¥ ajog, ④t log ,

IIsi: '

i'

" ÷÷÷ .

March 19, 2018E¥e = log

log X - logy

I 109×4 ttzlogxy - 3log×Z ¥1091logy

109×4"

+ log ,,Yk - logxz'

109×2+109×442 - log ×Z'

logy @y" ) - log ,,Z

'

log , )

March 19, 2018Expand3

iI

= logs U"

- log,

WV"

=3 log su - ( logs W t logsV " )=3 log su - logs.

w - 4 logs V

'"'

logs 42 - 9

iE-Hlogs 5 - logs 24

I - log 524 pmI - logs (6 - 4) =/ - Cogs.Gt logs4)

I - I. I -

.9 he - I

March 19, 2018

March 19, 2018

March 19, 2018

March 19, 2018